What value will come in place of question mark (?) in the questions given below?
`2 7/9 + 3/4 + 1 4/5 = ?`

Options

A. `5 43/180`
B. `5 59/180`
C. `5 49/90`
D. `4 19/90`

Answer

To solve the expression \(2 \frac{7}{9} + \frac{3}{4} + 1 \frac{4}{5}\), we will follow these steps:

### Step 1: Convert Mixed Numbers to Improper Fractions
First, we need to convert the mixed numbers into improper fractions.

- For \(2 \frac{7}{9}\):
\[ 2 \frac{7}{9} = \frac{2 \times 9 + 7}{9} = \frac{18 + 7}{9} = \frac{25}{9} \]

- For \(1 \frac{4}{5}\):
\[ 1 \frac{4}{5} = \frac{1 \times 5 + 4}{5} = \frac{5 + 4}{5} = \frac{9}{5} \]

Now, we can rewrite the expression:
\[ \frac{25}{9} + \frac{3}{4} + \frac{9}{5} \]

### Step 2: Find the Least Common Multiple (LCM)
Next, we need to find the LCM of the denominators \(9\), \(4\), and \(5\).

- The prime factorization of \(9\) is \(3^2\).
- The prime factorization of \(4\) is \(2^2\).
- The prime factorization of \(5\) is \(5^1\).

The LCM is:
\[ LCM = 3^2 \times 2^2 \times 5^1 = 9 \times 4 \times 5 = 180 \]

### Step 3: Convert Each Fraction to Have a Common Denominator
Now we will convert each fraction to have the common denominator of \(180\).

- For \(\frac{25}{9}\):
\[ \frac{25}{9} = \frac{25 \times 20}{9 \times 20} = \frac{500}{180} \]

- For \(\frac{3}{4}\):
\[ \frac{3}{4} = \frac{3 \times 45}{4 \times 45} = \frac{135}{180} \]

- For \(\frac{9}{5}\):
\[ \frac{9}{5} = \frac{9 \times 36}{5 \times 36} = \frac{324}{180} \]

### Step 4: Add the Fractions
Now we can add the fractions:
\[ \frac{500}{180} + \frac{135}{180} + \frac{324}{180} = \frac{500 + 135 + 324}{180} = \frac{959}{180} \]

### Step 5: Convert to Mixed Number
Now we convert \(\frac{959}{180}\) into a mixed number:
- Divide \(959\) by \(180\):
- \(959 \div 180 = 5\) remainder \(59\).

Thus, we can write:
\[ \frac{959}{180} = 5 \frac{59}{180} \]

### Final Answer
The value that will come in place of the question mark (?) is:
\[ 5 \frac{59}{180} \]

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